Generalisation of the rainbow neighbourhood number and k-jump colouring of a graph

Title

Generalisation of the rainbow neighbourhood number and k-jump colouring of a graph

Creator

Kok J.; Naduvath S.; Mphako-Banda E.G.

Description

In this paper, the notions of rainbow neighbourhood and rainbow neigh-bourhood number of a graph are generalised and further to these general-isations, the notion of a proper k-jump colouring of a graph is also intro-duced. The generalisations follow from the understanding that a closed k-neighbourhood of a vertex v ? V (G) denoted, Nk [v] is the set, Nk [v] = {u: d(v, u) ? k, k ? N and k ? diam(G)}. If the closed k-neighbourhood Nk [v] contains at least one of each colour of the chromatic colour set, we say that v yields a k-rainbow neighbourhood. 2020, Eszterhazy Karoly College. All rights reserved.

Source

Annales Mathematicae et Informaticae, Vol-52, pp. 147-158.

Date

2020-01-01

Publisher

Eszterhazy Karoly College

Subject

K-jump colouring; K-rainbow neighbourhood; K-rainbow neighbourhood number

Coverage

Kok J., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, 560029, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, 560029, India; Mphako-Banda E.G., School of Mathematical Sciences, University of Witswatersrand Johannesburg, South Africa

Rights

All Open Access; Gold Open Access; Green Open Access

Relation

ISSN: 17875021

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.33039/ami.2020.02.003

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